You like going into detail, don't you? It'd be my pleasure to provide you some!

Here's the loading gauge for the european railroad (G1 is international, G2 is Germany):

We're talking so called normal track gauge which is for most of Europe 1435mm - the Russians have wider gauge to prevent the invaders from using their network.

As you see the widest space on a rail car would be 3150mm. At the same time I read that the widest space in the cabin of a 737 is 3530mm. That would mean the fuselage is a tad wider, ergo it wouldn't fit by at least 400mm. If they absolutely can't fly it, they will put it on a barge, or take it on the Autobahn.

I work for a company that makes very big, commercial aircraft engines. Our largest engines require two trucks. The fan assembly goes on one, and the propulsor assembly goes on another. There have been mishaps which have put engines in muddy corn fields.